I agree, it'd be nice to figure out a way to either plug a Bluetooth or Ethernet module there.
The Bluetooth module is easy, you can use the Arduino-compatible serial connector to connect it. A Bluetooth module needs Gnd, 3.3V, RX and TX. These are all there.
My thought was "something that fits there without some hacking or bodgy wires". The socket would be most likely placed so it aligns to the hole in the case and there's probably no direct replacement BT module that would match the socket pins. So we're either mount the module somewhere else and do some wiring or design a custom daughter board that can be plugged nicely, fit's the space
and is mounted securely for moving the whole unit. Not that someone would play american football with the PSU, but if it's portable then the construction must be prepared for thing you don't do with most of the bench equipment. Or at least it must be built like old school bench hardware, I'm pretty sure I can airdrop my Wavetek without a chute and it'll survive.